Solutions to
-equations on strongly
pseudo-convex domains with
-estimates

Osama Abdelkader & Shaban Khidr
Abstract:
We construct a solution to the
-equation on
a strongly pseudo-convex domain of a complex manifold.
This is done for forms of type
,
,
with values in a holomorphic vector bundle which is Nakano
positive and for complex valued forms of type
,
,
when the complex manifold is a Stein manifold.
Using Kerzman's techniques, we find the
-estimates,
,
for the solution.